Question

PROJECT 4 Estimation of the Population Mean of Soft Plaque Deposit (Confidence Interval of the Mean). Estimation of the Population Proportion of Soft Plaque Deposit (Confidence Interval of the Proportion). This project uses the sample data of the experiment Atassi (A-1), shown here. Assume the variable, soft plaque deposit index, is approximately normally distributed. In a study of the oral home care practice and reasons for seeking dental care among individuals on renal dialysis, Atassi (A-1) studied 90 subjects on renal dialysis. The oral hygiene status of all subjects was examined using a plaque index with a range of 0 to 3 (0=no soft plaque deposits, 3=an abundance of soft plaque deposits). The following table shows the plaque index scores for all 90 subjects. 1.17; 2.50; 2.00; 2.33; 1.67; 1.33; 1.17; 2.17; 2.17; 1.33; 2.17; 2.00; 2.17; 1.17; 2.50; 2.00; 1.50; 1.50; 1.00; 2.17; 2.17; 1.67; 2.00; 2.00; 1.33; 2.17; 2.83; 1.50; 2.50; 2.33; 0.33; 2.17; 1.83; 2.00; 2.17; 2.00; 1.00; 2.17; 2.17; 1.33; 2.17; 2.50; 0.83; 1.17; 2.17; 2.50; 2.00; 2.50; 0.50; 1.50; 2.00; 2.00; 2.00; 2.00; 1.17; 1.33; 1.67; 2.17; 1.50; 2.00; 1.67; 0.33; 1.50; 2.17; 2.33; 2.33; 1.17; 0.00; 1.50; 2.33; 1.83; 2.67; 0.83; 1.17; 1.50; 2.17; 2.67; 1.50; 2.00; 2.17; 1.33; 2.00; 2.33; 2.00; 2.17; 2.17; 2.00; 2.17; 2.00; 2.17; This project has two parts. Part I. Confidence Interval on the Mean. Show the sample data. Describe the purpose for computing a confidence interval for the mean. (What you are setting out to find) Pick a confidence level of your choice. 1. Compute a sample mean. 2. Describe the variable. 3. Describe the confidence level you are taking and its specific meaning. 4. Show the confidence interval formula that you are using. 5. Show the reliability coefficient (critical value). 6. Show all the pertinent computations using the equation editor. 7. Draw a conclusion in the context of the experiment. Part II. Confidence Interval on the Proportion. Show the sample data. Describe the purpose for computing a confidence interval on the Proportion (What you are setting out to obtain) Pick a confidence level of your choice. 1. Compute a sample proportion of your choice (pick a certain index, count how many times it comes up in the sample, divide this frequency by sample size). 2. Describe the variable. 3. Describe the confidence level you are taking and its specific meaning. 4. Show the confidence interval formula that you are using. 5. Show the reliability coefficient (critical value). 6. Show all the pertinent computations using the equation editor. 7. Draw a conclusion in the context of the experiment.

Answer 1

Part I

1)

The sample mean of soft plaque deposit index is calculated using the excel function =AVERAGE()

2)

The variable used here is the mean soft plaque deposite index which is the average of sample soft plaque deposite index which takes the value 0 to 3 ("0" for no soft plaque deposite and "3" for an abundance of soft plaques deposite

3)

Lets taking confidence level,

A 95% confidence level means that 95% of the time estimates of the interval of sample mean will include the population mean

4)

The confidence inteval for mean is define as,

where is the mean, is the sample standard deviation, is the sample size and value is determined by confidence level which obtain from z distribution table.

4)

Thr critical value or reliability coefficient is 1.96 for 95% confidence interval which obtained fro z distribution table

5)

For 95% confidence level,

7)

the mean of the soft plaque deposite index is 1.81722 and the 95% confidence interval is [1.7010, 1.9334] which means 95% of the time the sample mean will lie in this interval or we can say the 95% of the provided data values are within this interval.

Part II)

1)

Let we want to compute the sample proportion for index = 2.17

The frequency of 2.17 in sample is obtained using excel function =COUNTIF(range,2.17)

The sample proportion is,

2)

The variable used here is the proportion of soft plaque deposite index which is the proportion of sample soft plaque deposite index

3)

The confidence level for proportion is called confidence coefficient which is same to confidence level. Lets' take the confidence coefficient 0.95. The 0.95 confidence coefficient mean 95% confidence level.

4)

The confidence interval is,

5)

z value = 1.96 for 95% confidence level

6)